Publication 535 states the following regarding who can claim depletion:
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Who Can Claim Depletion?
If you have an economic interest in mineral property or standing timber, you can take a deduction for depletion. More than one person can have an economic interest in the same mineral deposit or timber. In the case of leased property, the depletion deduction is divided between the lessor and the lessee.

You have an economic interest if both the following apply.

•You have acquired by investment any interest in mineral deposits or standing timber.

•You have a legal right to income from the extraction of the mineral or cutting of the timber to which you must look for a return of your capital investment.

A contractual relationship that allows you an economic or monetary advantage from products of the mineral deposit or standing timber is not, in itself, an economic interest. A production payment carved out of, or retained on the sale of, mineral property is not an economic interest.
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So, my question is, if the t/p inherited the right to the oil royalty, was it aquired by "investment"? How about if the t/p was gifted the royalties?